Question

1. An industrial area has several companies that use similar chemicals. Groundwater in this area has been found to be contaminated, and several companies are disputing who is responsible. (The responsible party must pay for remediation.) Two of the chemicals used by several companies are TCE and dioxane, but the companies often use different ratios of these chemicals. One company uses 3.6 times more TCE than dioxane, and the standard deviation of the TCE:dioxane ratio in its supply drums was 0.3. This company claims it isn’t responsible for remediation, because the ratio of TCE:dioxane in water samples is different from what the company uses. Samples of groundwater from 12 wells in the area yielded the following TCE:dioxane ratios:

3.1       2.6       4.5       6.2       4.2       3.3       1.2       3.6       5.9       2.7       3.7       3.8      

Can the company “prove” that there is less than a 5% chance that they contributed to the groundwater contamination?   Explain your answer using statistical justification.

Answer 1

Null hypothesis H0: Population Mean TCE:dioxane ratios in groundwater is 3.6

Alternative hypothesis H0: Population Mean TCE:dioxane ratios in groundwater is not 3.6.

Since we know the population standard deviation of company TCE:dioxane ratio, we will use z test to verify the claim.

Standard error of mean TCE:dioxane ratios = 0.3 / = 0.0866

Sample mean = (3.1 + 2.6 + 4.5 + 6.2 + 4.2 + 3.3 + 1.2 + 3.6 + 5.9 + 2.7 + 3.7 + 3.8 ) /12 = 3.733333

Test statistic, z = (Observed mean - Hypothesized mean) / Standard error

= (3.733333 - 3.6) / 0.0866

= 1.54

P(z > 1.54) = 0.0618

For two tail test, P-value = 2 * 0.0618 = 0.1236

Since p-value is greater than the significance level of 5%, we fail to reject null hypothesis H0 and conclude that there is insufficient evidence that population Mean TCE:dioxane ratios in groundwater is not 3.6.

Thus, the company cannot “prove” that there is less than a 5% chance that they contributed to the groundwater contamination.